Mesh-Free Hydrodynamics in Galaxy and Star Formation

Abstract:

Star and galaxy formation are fundamental to our understanding of the Universe. Despite decades of efforts by both observers and theorists there is no comprehensive theory for either due to the complexity of the physical processes involved (e.g., turbulence, gravity, radiation, magnetic fields). This makes numerical simulations the key tool for understanding how exactly these processes interact and what effect they have on the evolution of the Universe. However, simulations face significant challenges due to the extreme dynamic range and deep time hierarchy of the problem, making a simulation extremely costly even on the largest supercomputers. In this talk I will review some of the numerical methods used by state-of-the-art star and galaxy formation simulations (STARFORGE & FIRE) to tackle these challenges.

Bio:

I am a theoretical and computational astrophysicist. I am mostly interested in the rich phenomena of star formation. I utilize both analytical and numerical tools to answer questions like:

What regulates star formation?
What sets the characteristic mass of stars?
Why are stars clustered?
What determines the properties of stellar binaries?
How is star formation different in other galaxies?

These questions have far reaching implications beyond the field of star formation. The interpretation of observed starlight from any extragalactic sources rely on our understanding and assumptions about star formation. Similarily answering these questions would greatly enhance our knowledge about the circumstances of planet formation.

I am originally from Hungary where I got my bachelor's and master's degrees in physics. I received my PhD in phyiscs from the California Institute of Technology and I am currently a Cottrell postdoctoral fellow at the University of Texas at Austin.

Summary:

Software:
- STARFORGE: Simulation of star formation
- FIRE: Simulation of galaxy formation
- GIZMO: Numerical code-base behind both
Challenges:
- Compressible turbulence
- Extreme dynamic range: individual stars to whole universe is 20 orders of magnitude
- Feedback from small scales
  - Wind/radiation bubbles, shock waves: .1-1 light years
  - Protostellar outflows (gas jets blow out when stars form)
  - Supernovae have a large effect radius (can affect galaxy clusters)
- Deep time hierarchy
  - Galaxy ~ 200Myr
  - Molecular cloud ~ 1Myr
  - Binary stars ~1 yr
- Multi-species fluid
  - Hydrogen + Helium
  - Chemistry from different elements; small by mass but big effect on thermodynamics
  - Dust, formed by heavy elements; attenuates radiation
  - Tracking chemical species significantly increases memory use
Numerical approach
- Conservative hydro method
- Adaptive spatial scaling
- Advanced adaptive timestepping
- Sub-grid prescriptions
Smoothed Particle Hydrodynamics (SPH)
- Lagrangian method: particles tracked individually as they flow over the grid
- Particle positions smoothed using Gaussian kernel
- Challenges: numerically unstable but manageable using artificial viscosity terms
Adaptive Mesh Refinement (AMR)
- Eulerian fluid elements
- Mesh elements have different sizes
- Grid is structured (good mapping to compute hardware) but hierarchical to capture different scales
- Can incorporate Lagrangian elements to deal with very dense regions of space
- Key challenges:
  - Is that the grid is fixed in space, which has high errors for fast-moving flows
  - Shape of geometry imprints itself on the pattern of errors in the result
Quasi-Lagrangian Godunov methods (MF*)
- Mesh moves with the flow
- No preferred mesh geometry
- Volume re-meshed periodically
- Appropriate for complex flows
  - Rotating disk of many particles: star system, galaxy
  - Turbulent flows: Kelvin-Helmholtz, Rayleigh-Taylor instabilities
- Their implementation
  - Good weak scaling upto 10^10 elements / 10^5 CPUs
  - Strong calling: > 3e10^4 cell/core
  - FIRE: > 7E10^4 cell/core
Star formation process
- Gravity pulls gas in, stars form, blow out remaining gas
- Hard to model because gravity is a long-range force
  - Need to “soften” gravity to reduce need for very small time steps
  - Use a Tree-Particle-Mesh method
    - Tree of meshes
    - Short-range forces done within mesh
    - Long-range forces done at various levels of precision across sub-trees of meshes
- Gravity + Magnetohydrodynamics violates some conservations in MF* methods, so special schemes develop to solve this
- Time-stepping
  - Different time scales
  - Don’t want to force all processes to use same tiny time step size
  - Time step must reflect the speed of causality in system (fast flows: tiny time steps)
  - Mesh moves with the flow, so acceleration also affects time step size
    - Need to focus on relative acceleration of different sub-elements (e.g. focus on Earth-moon relative acceleration separately from how sun accelerates them)
- Sink particles
  - When we see a gas cell converging into a single place, replace with a “sink particle”
  - The particle is a solar system and its dynamics are modeled using another model
  - These particles need to be coupled to mesh cells
Validation
- Different simulations disagree
- Make prediction for problems with an analytic solution
  - Most codes pass these tests
- Can compare simulations to observations
  - Mass spectrum of stars
  - Amount of hot gas in the galaxy